SS2 Dr. R. D. Kleeman on the Effect of the 



We have accordingly 



A 1 = -9776^, A 2 -'2244^, A 3 = '07246^, and A 4 = -0219^ 



X X X lb 



and hence equation (9) by means of equation (10) becomes 



•876X2|^)| =pn u 



x y dx J t 



On comparing this equation — which represents the effect 

 of all the molecules in the slab B x with equation (3) — which 

 represents the effect of a single molecule, we see that the 

 difference in form consists of the factor *876 occurring in 

 one equation where the factor 1 occurs in the other. Since 



KY /3 



P 



where p denotes the density of the substance and m a the 

 absolute mass of a molecule, equation (11) may be written 



^raes)},-? <» 



The foregoing equation may be thrown into a form which 

 is more convenient. In a previous paper * it was shown that 



P _<*£_ _ o^E 



r?i ~ dv~ p dp' 



where U denotes the energy expended in overcoming the 

 molecular attraction on separating the molecules of a gram 

 of matter by an infinite distance from one another. The 

 equation then becomes 



•876x6 



•d(^)=dV (13) 



\p 



Integrating it we obtain 



•876 x6X 



=u+c, 



m l/3p2/3 

 a r 



where C is an arbitrary constant. The value of the constant 

 C may be determined from the following considerations. 

 When the density of the substance is infinitely small, or x is 



infinitely great, U = 0and A 2 = 0. The expression may be 



K . . P" /3 



written -^, where K is a constant, if we assume that the 



* Proc, Camb. Phil. Soc. vol. xvi. pt. vi. pp. 543-546. 



